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When we throw a tennis ball into a lake for my dog she knows that if she swims straight for it she'll take longer to get to the ball. Instead, sheruns along the beach for a short distance and then turns and swims for the ball.Let's say we throw the ball so that it lands 15 meters out into the water and 5 meters to the right of where we're standing. Draw a picture of this scenario.Finally, let's say that the dog runs at a rate of 2.5 meters per second and swims at a rate of 1 meters per second.(A) If the dog were to swim directly for the ball how long will it take? Recall that distance is equal to rate multiplied by time.Direct Swim Time = seconds.(B) If the dog were to run down the beach and make a 90 degree turn and then swim directly for the ball how long would it take to get to the ball?Time for longest run and 90 degree turn to swim = seconds.(C) My dog is smarter than either of the answers in parts (A) or (B). She knows that there is a better solution. Let be the amount of running that shedoes down the beach (clearly r is less than 5 and greater than 0). The trip has now been broken into two parts: a running leg of length x meters and aswimming leg at some angle to the beach. What is the length of the swimming leg as a function of r?Length of swimming leg =(D) Write a function T(r) that expresses the total time to get to the ball in terms of how far she runs down the beach.T(r):

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